Scale-Dependent Dispersion Behavior of Electrode–Piezoelectric–Electrode Sandwich Nanoplates Considering Surface Effects

This paper presents an analysis of wave dispersion behavior in electrode–piezoelectric–electrode sandwich structures, considering surface effects (SE). The sandwich structure was situated atop an orthogonally anisotropic viscoelastic substrate. This paper aims to explore the surface effects on the dispersion characteristics of piezoelectric sandwich nanoplates embedded with viscoelastic substrates, integrating frequency-wave number curves and phase velocity-wave number curves. The displacement field of the nanoplate was derived using the sinusoidal shear deformation theory, and governing equations were established through Hamilton’s principle and surface constitutive equations. Subsequently, equations of motion were obtained based on the nonlocal strain gradient theory (NSGT), and characteristic equations were developed using harmonic solutions. The study thoroughly examined the effects of scale, viscoelasticity, and surface properties on wave propagation characteristics. The results reveal that scale effects significantly influence the dispersion curves of nanoplates, depending on the wave number, and emphasize the necessity of considering the surface effects of electrode layers. Notably, a reduction in thickness leads to an upward trend in both frequency and phase velocity curves. Furthermore, the Winkler modulus and shear modulus play a pivotal role in enhancing frequency stiffness, while increases in the damping coefficient and voltage result in a decrease in both frequency and phase velocity.